Unfortunately they deleted the EWR taxi rate schedule from the EWR website several months ago, so we have no idea how much a taxi would be.

My guess is somewhere in the $30-50 range with toll and tip, though.

I don't believe there is a direct bus service. In fact, all of the public transit directions on the Cape Liberty website involve a taxi for the last leg:

http://www.cruiseliberty.com/dirpark.htm